[R] Orthogonal Polynomials
ripley@stats.ox.ac.uk
ripley at stats.ox.ac.uk
Wed Oct 9 08:28:57 CEST 2002
The difference is just normalization (and that the tables are transposed
in your example). That is, R uses orthonormal polynomials, and tables of
orthogonal polynomials also have normalizing coefficients.
Normalization should not affect the least-squares fitting, but it does
make interpretation of the coefficients easier.
On Tue, 8 Oct 2002, Bliese, Paul D MAJ WRAIR-Wash DC wrote:
> Looking to the wonderful statistical advice that this group can offer.
>
> In behavioral science applications of stats, we are often introduced to
> coefficients for orthogonal polynomials that are nice integers. For
> instance, Kirk's experimental design book presents the following
> coefficients for p=4:
>
> Linear -3 -1 1 3
> Quadratic 1 -1 -1 1
> Cubic -1 3 -3 1
>
> In R orthogonal polynomials are not integers. For instance, in R where p =4:
>
> > poly(c(1:4),3)
> 1 2 3
> [1,] -0.6708204 0.5 -0.2236068
> [2,] -0.2236068 -0.5 0.6708204
> [3,] 0.2236068 -0.5 -0.6708204
> [4,] 0.6708204 0.5 0.2236068
>
> Where, of course, column 1 is linear, column 2 Quadratic and 3 cubic.
>
> My experience is that the coding scheme used in R works "better" than the
> integer scheme discussed in Kirk for many regression type analyses.
>
> Can anyone enlighten me as to why?
>
> Thanks,
>
> Paul Bliese
> Walter Reed Army Institute of Research
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--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
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